Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main3 {

	public static void main(String[] args) throws Throwable {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//		BufferedReader br = new BufferedReader(new FileReader("out"));
		StringTokenizer st = new StringTokenizer(br.readLine());
		PrintWriter out = new PrintWriter(System.out);
		int n = Integer.parseInt(st.nextToken());
		int m = Integer.parseInt(st.nextToken());
		int[][] goal = new int[n][m];
		for (int i = 0; i < goal.length; i++) {
			st = new StringTokenizer(br.readLine());
			for (int j = 0; j < goal[i].length; j++) {
				goal[i][j] = Integer.parseInt(st.nextToken());
			}
		}
		int minRow[] = new int[n];
		int minCol[] = new int[m];
		for (int i = 0; i < n; i++) 
		{
			int min = Integer.MAX_VALUE;
			for (int j = 0; j < m; j++) 
			{
				min = Math.min(min, goal[i][j]);
			}
			minRow[i] = min;
		}
		for (int i = 0; i < m; i++) 
		{
			int min = Integer.MAX_VALUE;
			for (int j = 0; j < n; j++) 
			{
				min = Math.min(min, goal[j][i]);
			}
			minCol[i] = min;
		}
		if(m>=n)
		{

			int[] rowInc = new int[n];
			int[] colInc = new int[m];
			int res = 0;
			for (int i = 0; i < n; i++) 
			{
				rowInc[i] = minRow[i];
				res += rowInc[i];
			}
			for (int i = 0; i < m; i++) 
			{
				int min = Integer.MAX_VALUE;
				for(int j = 0;j<n;j++)
				{
					min = Math.min(min, goal[j][i]-rowInc[j]);
				}
				colInc[i] = min;
				res += min;
			}
			for (int i = 0; i < n; i++) 
			{
				for (int j = 0; j < m; j++) 
				{
					if(rowInc[i]+colInc[j] != goal[i][j])
					{
						System.out.println(-1);
						return;
					}
				}
			}
			out.append(res+"\n");
			for (int i = 0; i < rowInc.length; i++) {
				while(rowInc[i]-->0)
				{
					out.append("row "+(i+1)+"\n");
				}
			}
			for (int i = 0; i < colInc.length; i++) {
				while(colInc[i]-->0)
				{
					out.append("col "+(i+1)+"\n");
				}
			}
		}
		else
		{

			int[] rowInc = new int[n];
			int[] colInc = new int[m];
			int res = 0;
			for (int i = 0; i < m; i++) 
			{
				colInc[i] = minCol[i];
				res += colInc[i];
			}
			for (int i = 0; i < n; i++) 
			{
				int min = Integer.MAX_VALUE;
				for(int j = 0;j<m;j++)
				{
					min = Math.min(min, goal[i][j]-colInc[j]);
				}
				rowInc[i] = min;
				res += min;
			}
			for (int i = 0; i < n; i++) 
			{
				for (int j = 0; j < m; j++) 
				{
					if(rowInc[i]+colInc[j] != goal[i][j])
					{
						System.out.println(-1);
						return;
					}
				}
			}
			out.append(res+"\n");
			for (int i = 0; i < rowInc.length; i++) {
				while(rowInc[i]-->0)
				{
					out.append("row "+(i+1)+"\n");
				}
			}
			for (int i = 0; i < colInc.length; i++) {
				while(colInc[i]-->0)
				{
					out.append("col "+(i+1)+"\n");
				}
			}
		}
		out.flush();
	}

}